(A) Cumulative distribution of p-values for association tests across approximately 850 loci. The sequenced haplotypes at each locus were treated as alleles (after eliminating singleton polymorphisms), and the significance of genotype–phenotype associations was tested using Kruskal–Wallis tests in the case of flowering time (a continuous trait), and using χ2 tests in the case of resistance (a binary trait). Under the null hypothesis of no association, the cumulative distribution should be a straight line: the observed distributions are all heavily skewed towards zero.
(B) The cumulative distribution of p-values for association with pathogen resistance, with and without correction for population structure using the program STRAT [13]. The false positive rate is decreased for avrPph3, but is unaffected for the other two phenotypes.
(C) The cumulative distribution of p-values for association with flowering time, with and without correction for population structure. ANOVA was used instead of the nonparametric Kruskal–Wallis test to make it possible to use population structure as cofactor (cf. [14]). The distribution for ANOVA with accessions from Finland and northern Sweden removed is also shown (“ANOVA − northern”). The false positive rate is decreased using both approaches.

To help determine which associations were real and which were due to population structure, the most significantly associated haplotypes (based on fragment-wise Kruskal–Wallis; see Materials and Methods) were clustered based on similarity in the list of accessions that carry each haplotype.
(A) The tree shows the resulting cluster with tips colored according to average flowering time among the accessions that carry the haplotype corresponding to each tip (the scale is given on the right along with a histogram showing the distribution of flowering time across the 95 accessions).
(B) The matrix shows the membership list for each haplotype. Each column corresponds to the haplotype (tip) in the tree above it; accessions highlighted in red carry the haplotype significantly associated with flowering time. The tree thus illustrates the clustering of the columns of the matrix: clustering was done based on pairwise distance as measured by the absolute value of the correlation in membership between columns. Phenotypes of the accessions are given on the right, and the rows of the matrix (i.e., the accessions) have been clustered based on pairwise Hamming distance. It is evident that most of the significant haplotypes, regardless of position in the genome, share similar membership lists that include the accessions from Finland and northern Sweden. On the other hand, the clusters corresponding to the known major alleles of FRI are unique, indicating that these are indeed true positives.

The columns on the left give the genotype and associated phenotype for four loci, for each of the 95 accessions. The four loci are the flowering time locus FRI (+, wild-type; 1, Ler null allele; 2, Col null allele [9]), for which the associated phenotype is flowering time in long-day conditions without vernalization (late flowering is indicated by height and color of bar), and the three pathogen resistance loci Rps5, Rpm1, and Rps2 (+, wild-type; −, null allele [10,11,12]), for which the associated phenotypes are hypersensitive response to the appropriate bacterial avr gene (red indicates resistance, black indicates susceptibility, and missing data are indicated by missing bar). The tree on the right illustrates the genetic relationships between the accessions [8]. It is clear that phenotypes and genotypes are correlated, genome-wide.

For flowering time (A), four different statistical methods were used (described in Materials and Methods): Voronoi focusing on “late” alleles (magenta line), Voronoi focusing on “early” alleles (blue line), CLASS (green line), and fragment-based Kruskal–Wallis tests (red line; see also Figure 2). For pathogen resistance (avrRpm1 [B], avrRpt2 [C], and avrPph3 [D]), only the last two tests were used. Higher peaks indicate stronger association (the y-axes are proportional to the negative log p-values, but have been normalized to the highest value within each test). The dotted lines correspond to the 95% percentile and are mainly intended to facilitate comparison between figures. Yellow vertical lines indicate the positions of the appropriate candidate loci. Peaks occur at these loci for all methods, but are otherwise distributed throughout the genome.

For each locus (FRI [A], Rpm1 [B], Rps2 [C], and Rps5 [D]), the bottom panel shows the pattern of association using all available fragment markers around the locus (the position of which is given by a grey vertical line), and the panels above show the effect of successively reducing the marker density so that no markers are within 10, 25, 50, and 100 kb (FRI only) of the causative polymorphisms. The dotted grey line represents the 95th percentile of all associations across the genome. Because we used an association statistic that utilizes the pattern of haplotype sharing across multiple fragments, the relative significance of any particular fragment may change depending on the presence or absence of other fragments. The FRI region (A) remains strongly associated with flowering time even for the lowest marker density, while the signal of association around the R genes (B–D) disappears as one goes from 10- to 25-kb spacing.